1. Field of the Invention
This invention relates to a method for representing digitized scanned image data, and more particularly, to a method for representing digitized data of a highly curved structure obtained by a non-intrusive cross-sectional image generating device.
2. Related Art
In a number of fields, including the field of medicine, computer-assisted tomography (CT), magnetic resonance (MR), and ultrasonic scanners have been employed to generate cross-sectional images of the interior of objects in great detail but in a non-intrusive manner. For example, a CT scanner consists of an x-ray machine and a computer. The scanner takes x-rays in thin two-dimensional cross-sectional "slices". Digitized data representing each "slice" is recorded by the computer and can be displayed on a graphics screen. One such scanner is the General Electric Model 9800 CT Scanner. A CT examination usually consists of a series of these cross-sectional views, each slice adjacent to the next (similar to slices from a loaf of bread). Similar slices can be taken by MR or ultrasonic scanning.
Such scans have been particularly useful in the medical field, where such digitized scan data has been reformatted to provide synthesized images of a scanned body structure in a plane or along a curve different from the plane of the original scanned images.
For example, the reformation of digitized data from such scans has in the past been used to recast data from an axial CT scan of a spine. After reformation, a synthesized image of the spine can be viewed from the sagittal or coronal planes of the body, thus providing an internal cross-sectional "slice" oriented as a "front view" or a "side view" x-ray of the spine.
Another reformed view of such axial scan data that has proven useful in practice is a curved coronal view or a curved sagittal view of a curved structure such as the spine. In these views, the axial data is reformed to present a synthesized image that appears to be a side or front view of the internal spinal structure along a curve that follows the curvature of the spine. In effect, the image presented is a longitudinal cross-section of the spine that follows the curvature of the spine.
In generating such cross-sectional reformed images, it is necessary to create a mathematical model of a curve that conforms to the curvature of the scanned structure. The calculated curve is mapped onto the digitized image data in order to select proper components of that data to reform into a synthesized image. Past scanning systems have typically modeled a curved structure such as the spine by a single polynomial generated by the least-squares method applied to a number of data points selected by a user from an image of the complete spine.
The prior art approach to modeling curved structures has worked sufficiently well for such anatomical structures as the spine which are not highly curved. However, it is desirable to obtain CT, MR, or ultrasonic scanned images of other structures in the body, such as the mandible or maxilla. A problem arises with both of these structures because they exhibit a high degree of curvature. The techniques used in the prior art for modeling the curvature of a body structure often cannot be effectively applied to such highly curved structures.
For example, FIG. 1 shows the outline of a typical maxilla. The prior art least-squares method for generating a polynomial that best approximates a set of user-defined data points "outlining" a desired curve is not always able to generate a polynomial that will accurately trace the curvature of a typical maxilla. This reflects the inability of a least-square algorithm to fit a single polynomial to a set of discrete data points that contain squared or non-smooth corners (for example, the maxilla typically has approximately square corners). A second problem with the prior art data representation is that the polynomial used to represent the curve must be a mathematical function, so that for each "x" data point, there is one and only one "y" data point. Therefore, the prior art cannot deal with colinear points of the type shown along line A--A' in FIG. 1.
A further problem arises with respect to generating additional reformed images. Once the scanned structure has been mathematically modeled as a line or curve, the line or curve can be applied to the scanned image data to generate synthesized views of the scanned structure.
However, the basic mathematical model only provides a single "slice" of the curve structure upon which to synthesize an image. To synthesize further images corresponding to different "slices" through the scanned structure, the basic mathematical model can be manipulated to generate a family of curves which can then be applied to the scanned data image. For example, FIG. 2a graphically shows an initial curved line 20 generated for a spine. To generate additional views of the spine along different curves, additional curves 21 (shown as dotted lines in FIG. 2a) can be created by simple translation of the initial curve. This simple translation generally produces a family of curves that are approximately equidistant. However, the curved structure to be scanned may exhibit certain characteristics that will cause this technique to fail, as shown encircled in FIG. 2b, where the simple translation of the original curve will produce a family of curves that are not equidistant at all points, but instead merge.
An approach taken to solve this problem has been to generate a series of equidistant points along the original curve, and to create equal length lines perpendicular to those points to define a new set of points equidistant from the initial curve 20 and through which a new curve 22 can be constructed. This is diagrammatically shown in FIG. 2c. However, some problems persist with this technique when applying it to highly curved structures. If equally spaced perpendicular lines are generated for local tangents, difficulties arise for areas of high curvature. For example, as shown in FIG. 2d, the points defined by the ends of each perpendicular line may become out of order on the "inside" of an area of high curvature, while "outside" an area of high curvature the ends of the perpendicular lines do not accurately follow the curvature of the original curve.
Therefore, it is desirable to generate a smooth curve overlying a scanned image of a highly curved structure so that synthesized images of the scanned structure can be generated based on the curve. It is further desirable to be able to generate a family of curves each having its points equidistant from the initial curve.
It is an object of this invention to provide a means for representing an initial curve that conforms to a highly curved scanned structure, as well as to provide a means for generating a plurality of similar curves equidistant from the initial curve.